diff --git a/libsolidity/experimental/ast/Type.h b/libsolidity/experimental/ast/Type.h
index f98925684..dde41b1df 100644
--- a/libsolidity/experimental/ast/Type.h
+++ b/libsolidity/experimental/ast/Type.h
@@ -17,6 +17,7 @@
 // SPDX-License-Identifier: GPL-3.0
 #pragma once
 
+#include <cstddef>
 #include <set>
 #include <variant>
 #include <vector>
@@ -86,8 +87,8 @@ public:
 	}
 private:
 	friend class TypeSystem;
-	TypeConstructor(size_t _index): m_index(_index) {}
-	size_t m_index = 0;
+	TypeConstructor(std::size_t _index): m_index(_index) {}
+	std::size_t m_index = 0;
 };
 
 struct TypeConstant
@@ -119,8 +120,8 @@ public:
 	}
 private:
 	friend class TypeSystem;
-	TypeClass(size_t _index): m_index(_index) {}
-	size_t m_index = 0;
+	TypeClass(std::size_t _index): m_index(_index) {}
+	std::size_t m_index = 0;
 };
 
 struct Sort
@@ -141,13 +142,13 @@ struct Arity
 
 struct TypeVariable
 {
-	size_t index() const { return m_index; }
+	std::size_t index() const { return m_index; }
 	Sort const& sort() const { return m_sort; }
 private:
 	friend class TypeSystem;
-	size_t m_index = 0;
+	std::size_t m_index = 0;
 	Sort m_sort;
-	TypeVariable(size_t _index, Sort _sort): m_index(_index), m_sort(std::move(_sort)) {}
+	TypeVariable(std::size_t _index, Sort _sort): m_index(_index), m_sort(std::move(_sort)) {}
 };
 
 }
diff --git a/libsolidity/experimental/ast/TypeSystem.cpp b/libsolidity/experimental/ast/TypeSystem.cpp
index e6e65a110..5347b3d15 100644
--- a/libsolidity/experimental/ast/TypeSystem.cpp
+++ b/libsolidity/experimental/ast/TypeSystem.cpp
@@ -32,6 +32,8 @@
 
 #include <fmt/format.h>
 
+#include <unordered_map>
+
 using namespace solidity;
 using namespace solidity::frontend;
 using namespace solidity::frontend::experimental;
@@ -133,7 +135,7 @@ TypeSystem::TypeSystem()
 
 	m_primitiveTypeClasses.emplace(PrimitiveClass::Type, declarePrimitiveClass("type"));
 
-	for (auto [type, name, arity]: std::initializer_list<std::tuple<PrimitiveType, char const*, uint64_t>>{
+	for (auto [type, name, arity]: std::initializer_list<std::tuple<PrimitiveType, char const*, size_t>>{
 		{PrimitiveType::TypeFunction, "tfun", 2},
 		{PrimitiveType::Function, "fun", 2},
 		{PrimitiveType::Function, "itself", 1},
@@ -157,7 +159,7 @@ TypeSystem::TypeSystem()
 
 experimental::Type TypeSystem::freshVariable(Sort _sort)
 {
-	uint64_t index = m_numTypeVariables++;
+	size_t index = m_numTypeVariables++;
 	return TypeVariable(index, std::move(_sort));
 }